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  <div class="section" id="numpy-pmt">
<h1>numpy.pmt<a class="headerlink" href="#numpy-pmt" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.pmt">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">pmt</code><span class="sig-paren">(</span><em class="sig-param">rate</em>, <em class="sig-param">nper</em>, <em class="sig-param">pv</em>, <em class="sig-param">fv=0</em>, <em class="sig-param">when='end'</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/lib/financial.py#L163-L262"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.pmt" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the payment against loan principal plus interest.</p>
<div class="deprecated">
<p><span class="versionmodified deprecated">Deprecated since version 1.18: </span><a class="reference internal" href="#numpy.pmt" title="numpy.pmt"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pmt</span></code></a> is deprecated; for details, see NEP 32 <a class="reference internal" href="#rc2d922c8f780-1" id="id1">[1]</a>.
Use the corresponding function in the numpy-financial library,
<a class="reference external" href="https://pypi.org/project/numpy-financial">https://pypi.org/project/numpy-financial</a>.</p>
</div>
<dl class="simple">
<dt>Given:</dt><dd><ul class="simple">
<li><p>a present value, <a class="reference internal" href="numpy.pv.html#numpy.pv" title="numpy.pv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pv</span></code></a> (e.g., an amount borrowed)</p></li>
<li><p>a future value, <a class="reference internal" href="numpy.fv.html#numpy.fv" title="numpy.fv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fv</span></code></a> (e.g., 0)</p></li>
<li><p>an interest <a class="reference internal" href="numpy.rate.html#numpy.rate" title="numpy.rate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">rate</span></code></a> compounded once per period, of which
there are</p></li>
<li><p><a class="reference internal" href="numpy.nper.html#numpy.nper" title="numpy.nper"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nper</span></code></a> total</p></li>
<li><p>and (optional) specification of whether payment is made
at the beginning (<em class="xref py py-obj">when</em> = {‘begin’, 1}) or the end
(<em class="xref py py-obj">when</em> = {‘end’, 0}) of each period</p></li>
</ul>
</dd>
<dt>Return:</dt><dd><p>the (fixed) periodic payment.</p>
</dd>
</dl>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>rate</strong><span class="classifier">array_like</span></dt><dd><p>Rate of interest (per period)</p>
</dd>
<dt><strong>nper</strong><span class="classifier">array_like</span></dt><dd><p>Number of compounding periods</p>
</dd>
<dt><strong>pv</strong><span class="classifier">array_like</span></dt><dd><p>Present value</p>
</dd>
<dt><strong>fv</strong><span class="classifier">array_like,  optional</span></dt><dd><p>Future value (default = 0)</p>
</dd>
<dt><strong>when</strong><span class="classifier">{{‘begin’, 1}, {‘end’, 0}}, {string, int}</span></dt><dd><p>When payments are due (‘begin’ (1) or ‘end’ (0))</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray</span></dt><dd><p>Payment against loan plus interest.  If all input is scalar, returns a
scalar float.  If any input is array_like, returns payment for each
input element. If multiple inputs are array_like, they all must have
the same shape.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The payment is computed by solving the equation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fv</span> <span class="o">+</span>
<span class="n">pv</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">rate</span><span class="p">)</span><span class="o">**</span><span class="n">nper</span> <span class="o">+</span>
<span class="n">pmt</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">rate</span><span class="o">*</span><span class="n">when</span><span class="p">)</span><span class="o">/</span><span class="n">rate</span><span class="o">*</span><span class="p">((</span><span class="mi">1</span> <span class="o">+</span> <span class="n">rate</span><span class="p">)</span><span class="o">**</span><span class="n">nper</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>
</pre></div>
</div>
<p>or, when <code class="docutils literal notranslate"><span class="pre">rate</span> <span class="pre">==</span> <span class="pre">0</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fv</span> <span class="o">+</span> <span class="n">pv</span> <span class="o">+</span> <span class="n">pmt</span> <span class="o">*</span> <span class="n">nper</span> <span class="o">==</span> <span class="mi">0</span>
</pre></div>
</div>
<p>for <code class="docutils literal notranslate"><span class="pre">pmt</span></code>.</p>
<p>Note that computing a monthly mortgage payment is only
one use for this function.  For example, pmt returns the
periodic deposit one must make to achieve a specified
future balance given an initial deposit, a fixed,
periodically compounded interest rate, and the total
number of periods.</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="rc2d922c8f780-1"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
<dd><p>NumPy Enhancement Proposal (NEP) 32,
<a class="reference external" href="https://numpy.org/neps/nep-0032-remove-financial-functions.html">https://numpy.org/neps/nep-0032-remove-financial-functions.html</a></p>
</dd>
<dt class="label" id="rc2d922c8f780-2"><span class="brackets">2</span></dt>
<dd><p>Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May).
Open Document Format for Office Applications (OpenDocument)v1.2,
Part 2: Recalculated Formula (OpenFormula) Format - Annotated Version,
Pre-Draft 12. Organization for the Advancement of Structured Information
Standards (OASIS). Billerica, MA, USA. [ODT Document].
Available:
<a class="reference external" href="http://www.oasis-open.org/committees/documents.php">http://www.oasis-open.org/committees/documents.php</a>
?wg_abbrev=office-formulaOpenDocument-formula-20090508.odt</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>What is the monthly payment needed to pay off a $200,000 loan in 15
years at an annual interest rate of 7.5%?</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pmt</span><span class="p">(</span><span class="mf">0.075</span><span class="o">/</span><span class="mi">12</span><span class="p">,</span> <span class="mi">12</span><span class="o">*</span><span class="mi">15</span><span class="p">,</span> <span class="mi">200000</span><span class="p">)</span>
<span class="go">-1854.0247200054619</span>
</pre></div>
</div>
<p>In order to pay-off (i.e., have a future-value of 0) the $200,000 obtained
today, a monthly payment of $1,854.02 would be required.  Note that this
example illustrates usage of <a class="reference internal" href="numpy.fv.html#numpy.fv" title="numpy.fv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fv</span></code></a> having a default value of 0.</p>
</dd></dl>

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